Movement in the stock price is the only thing that causes intrinsic value to change. Provided the option price contains intrinsic value, the intrinsic value will move point-for-point with the stock price. Therefore, the more intrinsic value an option has as a percentage of its total price, the more it will behave like the stock price.
Figure 1. With the stock price at $37.00, the XYZ Jan 35 Call option has $2.00 of intrinsic value.
Figure 2. The stock price has dropped by $1.00. As such, the intrinsic value of the option has dropped by exactly the same amount.
Figure 3. The stock price has continued to fall to $34, which is below the $35 strike price. The option is now out-of-the-money (OTM) and there is no longer intrinsic value. The option price will now be behave according only to the characteristics of time value.